Details

sample68.0ms

Algorithm

intervals

Results

21.0ms	39×	body	1280	valid
17.0ms	58×	body	640	valid
9.0ms	159×	body	80	valid
4.0ms	22×	body	320	valid
4.0ms	97×	body	80	nan
1.0ms	10×	body	160	valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
6.8b	(pow (/ x (+ x y)) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series423.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (pow (/ x (+ x y)) x) x)
43.0ms	(/ x (+ x y))
245.0ms	(pow (/ x (+ x y)) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5002	1406

prune328.0ms

Filtered

181 candidates to 131 candidates (72.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	5	182

Merged error: 0.3b

Counts

182 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series824.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
187.0ms	(cbrt x)
174.0ms	(cbrt x)
283.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify176.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	367	612
1	1118	572
2	4404	551
3	5001	551

prune210.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.0b

Counts

81 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.1b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
48×	`log-prod` `*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+`
1×	`log-div` `div-exp` `log-pow` `div-inv`

Counts

4 → 95

Calls

4 calls:

3.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (+ x y))
181.0ms	(cbrt x)
190.0ms	(cbrt x)
76.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify141.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	360	861
1	982	830
2	4123	810
3	5001	810

prune360.0ms

Filtered

107 candidates to 88 candidates (82.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ x (pow (/ x (+ x y)) x)))
0.0b	(/ x (pow (/ x (+ x y)) x))
0.0b	(/ x (+ x y))
6.8b	(pow (/ x (+ x y)) x)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

756×	`times-frac`
462×	`*-un-lft-identity`
352×	`add-sqr-sqrt` `add-cube-cbrt`
306×	`unpow-prod-down`
96×	`associate-/r*`
55×	`distribute-lft-out`
49×	`add-exp-log`
37×	`associate-/r/`
32×	`div-exp`
24×	`div-inv`
18×	`flip3-+` `flip-+`
17×	`sqr-pow`
13×	`add-cbrt-cube`
10×	`pow-exp`
9×	`associate-/l*`
6×	`pow1`
5×	`cbrt-undiv` `pow-to-exp` `rec-exp` `1-exp`
4×	`add-log-exp`
3×	`pow-unpow` `frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `inv-pow`

Counts

4 → 485

Calls

4 calls:

24.0ms	(/ 1 (/ x (pow (/ x (+ x y)) x)))
10.0ms	(/ x (pow (/ x (+ x y)) x))
5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series711.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ x (pow (/ x (+ x y)) x)))
267.0ms	(/ x (pow (/ x (+ x y)) x))
45.0ms	(/ x (+ x y))
245.0ms	(pow (/ x (+ x y)) x)

simplify100.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1443	5433
1	5001	5056

prune803.0ms

Filtered

497 candidates to 302 candidates (60.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	497	4	501

Merged error: 0b

Counts

501 → 4

regimes57.0ms

Accuracy

99.4% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 6.1b

bsearch93.0ms

Steps

Iters	Range		Point
8	0.0009374011379127125	24.426543482179152	6.689089046971252
10	-0.022529268385055725	-1.121431443204481e-13	-0.022243402371581053

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	37	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

725.0ms	1456×	body	1280	valid
458.0ms	1518×	body	640	valid
264.0ms	4796×	body	80	valid
169.0ms	830×	body	320	valid
127.0ms	3079×	body	80	nan
57.0ms	459×	body	160	valid

Details

sample68.0ms

simplify116.0ms

prune5.0ms

localize7.0ms

rewrite32.0ms

series423.0ms

simplify73.0ms

prune328.0ms

localize15.0ms

rewrite21.0ms

series824.0ms

simplify176.0ms

prune210.0ms

localize15.0ms

rewrite17.0ms

series576.0ms

simplify141.0ms

prune360.0ms

localize7.0ms

rewrite80.0ms

series711.0ms

simplify100.0ms

prune803.0ms

regimes57.0ms

bsearch93.0ms

simplify2.0ms

end0.0ms

sample2.0s

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